Question

a car is traveling east. the graph shows the change in the velocity of the car over time, relative to the ground. during this period, what is the eastward acceleration of the car relative to the ground? 5 m/s² 25 m/s² 30 m/s² 150 m/s²

Explanation:

Step1: Recall the formula for acceleration

Acceleration \(a=\frac{\Delta v}{\Delta t}\), where \(\Delta v\) is the change in velocity and \(\Delta t\) is the change in time.

Step2: Determine \(\Delta v\) and \(\Delta t\) from the graph

From the graph, at \(t = 0\ s\), \(v_0=0\ m/s\) and at \(t = 6\ s\), \(v = 30\ m/s\). So \(\Delta v=v - v_0=30 - 0=30\ m/s\) and \(\Delta t=6 - 0 = 6\ s\).

Step3: Calculate the acceleration

Substitute into the formula: \(a=\frac{\Delta v}{\Delta t}=\frac{30}{6}=5\ m/s^{2}\)

Answer:

\(5\ m/s^{2}\) (First option)